Augmented Lagrangian alternating direction method for low-rank minimization via non-convex approximation

Augmented Lagrangian alternating direction method for low-rank minimization via non-convex... This paper concerns the low-rank minimization problems which consist of finding a matrix of minimum rank subject to linear constraints. Many existing approaches, which used the nuclear norm as a convex surrogate of the rank function, usually result in a suboptimal solution. To seek a tighter rank approximation, we develop a non-convex surrogate to approximate the rank function based on the Laplace function. An iterative algorithm based on the augmented Lagrangian multipliers method is developed. Empirical studies for practical applications including robust principal component analysis and low-rank representation demonstrate that our proposed algorithm outperforms many other state-of-the-art convex and non-convex methods developed recently in the literature. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png "Signal, Image and Video Processing" Springer Journals

Augmented Lagrangian alternating direction method for low-rank minimization via non-convex approximation

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Publisher
Springer London
Copyright
Copyright © 2017 by Springer-Verlag London
Subject
Engineering; Signal,Image and Speech Processing; Image Processing and Computer Vision; Computer Imaging, Vision, Pattern Recognition and Graphics; Multimedia Information Systems
ISSN
1863-1703
eISSN
1863-1711
D.O.I.
10.1007/s11760-017-1084-9
Publisher site
See Article on Publisher Site

Abstract

This paper concerns the low-rank minimization problems which consist of finding a matrix of minimum rank subject to linear constraints. Many existing approaches, which used the nuclear norm as a convex surrogate of the rank function, usually result in a suboptimal solution. To seek a tighter rank approximation, we develop a non-convex surrogate to approximate the rank function based on the Laplace function. An iterative algorithm based on the augmented Lagrangian multipliers method is developed. Empirical studies for practical applications including robust principal component analysis and low-rank representation demonstrate that our proposed algorithm outperforms many other state-of-the-art convex and non-convex methods developed recently in the literature.

Journal

"Signal, Image and Video Processing"Springer Journals

Published: Apr 6, 2017

References

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